Well I assigned a static IP address in my phone's WiFi and then enabled USB debugging and proceeded to ADB shell and did a ping to twitter.com and other websites to see a difference.
I must say that ping takes a lot of time to show the results, even the first one. I am not really sure why the ping is at 444ms when it almost took 4-5 seconds to display the first response (only for twitter). There's no traceroute command available so I cant traceroute from the android OS. I also did the ping with time command just in case.
PL2_sprout:/ $ time ping -c 5 openwrt.org
PING openwrt.org (139.59.209.225) 56(84) bytes of data.
64 bytes from wiki-01.infra.openwrt.org (139.59.209.225): icmp_seq=1 ttl=251 time=403 ms
64 bytes from wiki-01.infra.openwrt.org (139.59.209.225): icmp_seq=2 ttl=251 time=426 ms
64 bytes from wiki-01.infra.openwrt.org (139.59.209.225): icmp_seq=3 ttl=251 time=448 ms
64 bytes from wiki-01.infra.openwrt.org (139.59.209.225): icmp_seq=4 ttl=251 time=368 ms
64 bytes from wiki-01.infra.openwrt.org (139.59.209.225): icmp_seq=5 ttl=251 time=390 ms
--- openwrt.org ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4006ms
rtt min/avg/max/mdev = 368.367/407.556/448.309/27.801 ms
0m04.64s real 0m00.01s user 0m00.03s system
PL2_sprout:/ $ time ping -c 5 google.com
PING google.com (172.217.18.142) 56(84) bytes of data.
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=1 ttl=251 time=139 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=2 ttl=251 time=160 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=3 ttl=251 time=180 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=4 ttl=251 time=87.7 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=5 ttl=251 time=119 ms
--- google.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4012ms
rtt min/avg/max/mdev = 87.704/137.476/180.500/32.163 ms
0m04.17s real 0m00.02s user 0m00.01s system
PL2_sprout:/ $ time ping -c 5 twitter.com
PING twitter.com (104.244.42.65) 56(84) bytes of data.
64 bytes from 104.244.42.65: icmp_seq=1 ttl=251 time=444 ms
64 bytes from 104.244.42.65: icmp_seq=2 ttl=251 time=356 ms
64 bytes from 104.244.42.65: icmp_seq=3 ttl=251 time=395 ms
64 bytes from 104.244.42.65: icmp_seq=4 ttl=251 time=426 ms
64 bytes from 104.244.42.65: icmp_seq=5 ttl=251 time=424 ms
--- twitter.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 41696ms
rtt min/avg/max/mdev = 356.133/409.355/444.470/30.934 ms
0m42.73s real 0m00.02s user 0m00.02s system
PL2_sprout:/ $ time ping -c 5 microsoft.com
PING microsoft.com (40.113.200.201) 56(84) bytes of data.
--- microsoft.com ping statistics ---
5 packets transmitted, 0 received, 100% packet loss, time 4016ms
0m14.19s real 0m00.00s user 0m00.03s system
1|PL2_sprout:/ $ time ping -c 5 microsoft.com
PING microsoft.com (40.113.200.201) 56(84) bytes of data.
--- microsoft.com ping statistics ---
5 packets transmitted, 0 received, 100% packet loss, time 4007ms
0m14.04s real 0m00.02s user 0m00.02s system
1|PL2_sprout:/ $ time ping -c 5 yahoo.com
PING yahoo.com (72.30.35.9) 56(84) bytes of data.
64 bytes from media-router-fp1.prod1.media.vip.bf1.yahoo.com (72.30.35.9): icmp_seq=1 ttl=251 time=329 ms
64 bytes from media-router-fp1.prod1.media.vip.bf1.yahoo.com (72.30.35.9): icmp_seq=2 ttl=251 time=351 ms
64 bytes from media-router-fp1.prod1.media.vip.bf1.yahoo.com (72.30.35.9): icmp_seq=3 ttl=251 time=374 ms
64 bytes from media-router-fp1.prod1.media.vip.bf1.yahoo.com (72.30.35.9): icmp_seq=4 ttl=251 time=395 ms
--- yahoo.com ping statistics ---
5 packets transmitted, 4 received, 20% packet loss, time 4006ms
rtt min/avg/max/mdev = 329.085/362.474/395.243/24.713 ms
0m05.08s real 0m00.00s user 0m00.04s system
PL2_sprout:/ $ time ping -c 5 speedtest.net
PING speedtest.net (151.101.66.219) 56(84) bytes of data.
64 bytes from 151.101.66.219: icmp_seq=1 ttl=251 time=51.0 ms
64 bytes from 151.101.66.219: icmp_seq=2 ttl=251 time=135 ms
64 bytes from 151.101.66.219: icmp_seq=3 ttl=251 time=66.5 ms
64 bytes from 151.101.66.219: icmp_seq=4 ttl=251 time=68.0 ms
64 bytes from 151.101.66.219: icmp_seq=5 ttl=251 time=67.0 ms
--- speedtest.net ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4010ms
rtt min/avg/max/mdev = 51.023/77.691/135.720/29.690 ms
0m04.16s real 0m00.02s user 0m00.02s system
PL2_sprout:/ $ time ping -c 5 pakgamers.com
PING pakgamers.com (199.193.119.193) 56(84) bytes of data.
64 bytes from 199-193-119-193.static.hvvc.us (199.193.119.193): icmp_seq=1 ttl=251 time=433 ms
64 bytes from 199-193-119-193.static.hvvc.us (199.193.119.193): icmp_seq=2 ttl=251 time=355 ms
64 bytes from 199-193-119-193.static.hvvc.us (199.193.119.193): icmp_seq=3 ttl=251 time=375 ms
64 bytes from 199-193-119-193.static.hvvc.us (199.193.119.193): icmp_seq=4 ttl=251 time=397 ms
64 bytes from 199-193-119-193.static.hvvc.us (199.193.119.193): icmp_seq=5 ttl=251 time=421 ms
--- pakgamers.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4006ms
rtt min/avg/max/mdev = 355.144/396.832/433.876/28.898 ms
0m04.52s real 0m00.03s user 0m00.01s system
PL2_sprout:/ $ time ping -c 5 curiouscat.com
PING curiouscat.com (69.164.195.18) 56(84) bytes of data.
64 bytes from li110-18.members.linode.com (69.164.195.18): icmp_seq=1 ttl=251 time=303 ms
64 bytes from li110-18.members.linode.com (69.164.195.18): icmp_seq=2 ttl=251 time=337 ms
64 bytes from li110-18.members.linode.com (69.164.195.18): icmp_seq=3 ttl=251 time=347 ms
64 bytes from li110-18.members.linode.com (69.164.195.18): icmp_seq=4 ttl=251 time=371 ms
64 bytes from li110-18.members.linode.com (69.164.195.18): icmp_seq=5 ttl=251 time=396 ms
--- curiouscat.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4003ms
rtt min/avg/max/mdev = 303.954/351.389/396.055/31.102 ms
0m04.97s real 0m00.03s user 0m00.01s system
PL2_sprout:/ $ time ping -c 5 youtube.com
PING youtube.com (216.58.210.78) 56(84) bytes of data.
64 bytes from mct01s06-in-f78.1e100.net (216.58.210.78): icmp_seq=1 ttl=251 time=108 ms
64 bytes from mct01s06-in-f78.1e100.net (216.58.210.78): icmp_seq=2 ttl=251 time=198 ms
64 bytes from mct01s06-in-f78.1e100.net (216.58.210.78): icmp_seq=3 ttl=251 time=115 ms
64 bytes from mct01s06-in-f78.1e100.net (216.58.210.78): icmp_seq=4 ttl=251 time=136 ms
64 bytes from mct01s06-in-f78.1e100.net (216.58.210.78): icmp_seq=5 ttl=251 time=156 ms
--- youtube.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4011ms
rtt min/avg/max/mdev = 108.557/142.954/198.115/32.221 ms
0m04.25s real 0m00.02s user 0m00.01s system
PL2_sprout:/ $ time ping -c 5 google.com
PING google.com (172.217.18.142) 56(84) bytes of data.
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=1 ttl=251 time=85.3 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=2 ttl=251 time=111 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=3 ttl=251 time=132 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=4 ttl=251 time=155 ms
64 bytes from arn02s05-in-f142.1e100.net (172.217.18.142): icmp_seq=5 ttl=251 time=175 ms
--- google.com ping statistics ---
5 packets transmitted, 5 received, 0% packet loss, time 4011ms
rtt min/avg/max/mdev = 85.372/131.984/175.241/31.676 ms
0m04.28s real 0m00.00s user 0m00.03s system
Edit: I think the above ping tests properly show the behavior of twitter on my phone. It keeps trying to receive response but fails to do so. As you can also see most of the URLs get translated to some servers but twitter fails to do so. I don't know if this can be fixed because I have already reset my phone a couple of times because of the issue.